Kp,q-factorization of complete bipartite graphs

Let K_(m,n) be a complete bipartite graph with two partite sets having m and n vertices, respectively. A K_(p,q)-factorization of K_(m,n) is a set of edge-disjoint K_(p,q)-factors of K_(m,n) which partition the set of edges of K_(m,n). When p=i and q is a prime number, Wang, in his paper "On K_(1,k)-factorizations of a complete bipartite graph" (Discrete Math, 1994, 126; 359-364), investigated the K_(1,q)-factorization of K_(m,n) and gave a sufficient condition for such a factorization to exist. In the paper "K_(1,k)-factorizations of complete bipartite graphs" (Discrete Math, 2002, 259: 301-306), Du and Wang extended Wang's result to the case that q is any positive integer In this paper, we give a sufficient condition for K_(m,n) to have a K_(p,q)-factorization. As a special case, it is shown that the Martin's BAC conjecture is true when p: q=k: (k+1) for any positive integer k.